Finite Group Databasebeta

← #14288178

Subgroups — #14288178

Order 1920.

520 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 520 conjugacy classes of subgroups — too many to draw. Only its 83 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11756376C211yesmaximal, characteristic
2C3×C5×#448C211yesmaximal, characteristic, complemented
3#11751332C211yesmaximal, characteristic, complemented
4#11751329C211yesmaximal, characteristic, complemented
5#11746358C211yesmaximal, characteristic, complemented
6#11746289C211yesmaximal, characteristic, complemented
7#11746288C211yesmaximal, characteristic, complemented
8#10601766—31nomaximal, Hall
9C22×C3×C5×Q8C2211yescharacteristic
10C2×C3×C5×SD16—21no—
11C3×C5×#121C2211yescharacteristic
12C2×#6718—21no—
13#91828—21no—
14#91826—21no—
15D4×Dic15—21no—
16C2×#6714—21no—
17C2×#6714C2211yescharacteristic
18#91813C2211yescharacteristic
19#91787—21no—
20#91775—21no—
21#91774—21no—
22C3×C5×#103—21no—
23C3×C5×C22⋊C8C2211yescharacteristic
24#91119—21no—
25#91115—21no—
26#91115C2211yescharacteristic
27#91114C2211yescharacteristic
28#70973—51nomaximal, Hall
29#65951—31no—
30C5×#448D311yescharacteristic, complemented
31#65520—31no—
32#65517—31no—
33#64757—31no—
34#64688—31no—
35#64687—31no—
36C23×D15D411yescharacteristic
37C2×C3×C5×Q8—21no—
38C2×C3×C5×Q8—21no—
39C2×C3×C5×Q8—42no—
40C2×C3×C5×D4—21no—
41C2×C3×C5×D4D411yescharacteristic
42C22×C3×C4×C5—21no—
43C22×C3×C4×C5C2311yescharacteristic
44C2×#1220—21no—
45C2×#1220—21no—
46C22×Dic15—21no—
47C22×Dic15—21no—
48C22×Dic15D411yescharacteristic
49C2×Dic30D411yescharacteristic
50C3×C5×SD16—42no—
51C2×C3×C5×C8—21no—
52C3×C5×C4⋊C4D411yescharacteristic
53C3×C5×C22⋊C4—21no—
54#6719—21no—
55#6719—21no—
56#6718—42no—
57#6714—21no—
58#6714—21no—
59#6714—21no—
60#6714—21no—
61#6714—42no—
62C4⋊Dic15—21no—
63C4⋊Dic15D411yescharacteristic
64#6712—21no—
65C4×Dic15—21no—
66C2×C3⋊#168—21no—
67#5617—51no—
68C3×#448D511yescharacteristic, complemented
69#5231—51no—
70#5228—51no—
71#4537—51no—
72#4468—51no—
73#4467—51no—
74C22×C5×Q8C2×D311yescharacteristic
75C2×C5×SD16—21no—
76C5×#121C2×D311yescharacteristic
77C2×#689—61no—
78#4085—61no—
79#4083—61no—
80D4×Dic5—61no—
81C2×#685—31no—
82C2×#685—61no—
83#4070—31no—
84#4044—61no—
85#4032—61no—
86#4031—61no—
87C5×#103—21no—
88C5×C22⋊C8C2×D311yescharacteristic
89#3967—61no—
90#3963—31no—
91#3963—61no—
92C22⋊#168—31no—
93#1606—151noSylow
94C23×C3×C5—21no—
95C23×C3×C5C2×D411yescharacteristic
96C22×D15—21no—
97C22×D15—21no—
98C22×D15—21no—
99C22×D15—41no—
100C22×D15—41no—
101C3×C5×Q8—22no—
102C3×C5×Q8—22no—
103C3×C5×Q8—41no—
104C3×C5×Q8—41no—
105C3×C5×D4—41no—
106C3×C5×D4—41no—
107C3×C5×D4—41no—
108C2×C3×C4×C5—22no—
109C2×C3×C4×C5—21no—
110C2×C3×C4×C5—41no—
111C2×C3×C4×C5—41no—
112C2×C3×C4×C5—41no—
113C2×C3×C4×C5C2×D411yescharacteristic
114C2×C3×C4×C5C2×D411yescharacteristic
115#1220—81no—
116#1220—81no—
117C2×Dic15—21no—
118C2×Dic15—21no—
119C2×Dic15—21no—
120C2×Dic15—41no—
121C2×Dic15—41no—
122C2×Dic15—41no—
123C2×Dic15—41no—
124C2×Dic15—81no—
125Dic30—41no—
126C3×C5×C8—41no—
127C3⋊#168—41no—
128C22×C3×Q8C2×D511yescharacteristic
129C2×C3×SD16—21no—
130C3×#121C2×D511yescharacteristic
131C2×#216—101no—
132#939—101no—
133#937—101no—
134D4×Dic3—101no—
135C2×(C2×D3)⋊C4—51no—
136C2×(C2×D3)⋊C4—101no—
137#924—51no—
138#898—101no—
139#886—101no—
140#885—101no—
141C3×#103—21no—
142C3×C22⋊C8C2×D511yescharacteristic
143#835—101no—
144C3⋊#95—51no—
145C3⋊#95—101no—
146#830—51no—
147C23×D5—31no—
148C2×C5×Q8—21no—
149C2×C5×Q8—21no—
150C2×C5×Q8—42no—
151C2×C5×D4—21no—
152C2×C5×D4#6711yescharacteristic
153C22×C4×C5—21no—
154C22×C4×C5C22×D311yescharacteristic
155C2×C22⋊D5—61no—
156C2×C22⋊D5—61no—
157C22×Dic5—31no—
158C22×Dic5—61no—
159C22×Dic5—61no—
160C2×Dic10—31no—
161C5×SD16—42no—
162C2×C5×C8—21no—
163C5×C4⋊C4#6711yescharacteristic
164C5×C22⋊C4—21no—
165C22⋊Dic5—61no—
166C22⋊Dic5—61no—
167#689—122no—
168#685—61no—
169#685—61no—
170#685—61no—
171#685—61no—
172#685—122no—
173C4⋊Dic5—31no—
174C4⋊Dic5—61no—
175#683—61no—
176C4×Dic5—61no—
177C2×#168—61no—
178#538—151no—
179#451—151no—
180#448D1511yescharacteristic, complemented
181#393—151no—
182#328—151no—
183#327—151no—
184#323—151no—
185C22×C3×C5—21no—
186C22×C3×C5—21no—
187C22×C3×C5—41no—
188C22×C3×C5—41no—
189C22×C3×C5—41no—
190C22×C3×C5#12011yescharacteristic
191C22×C3×C5#13511yescharacteristic
192C22×C3×C5#13711yescharacteristic
193C2×D15—42no—
194C2×D15—41no—
195C2×D15—41no—
196C2×D15—41no—
197C2×D15—81no—
198C3×C4×C5—21no—
199C3×C4×C5—21no—
200C3×C4×C5—41no—
201C3×C4×C5—42no—
202Dic15—41no—
203Dic15—41no—
204Dic15—41no—
205Dic15—81no—
206C23×D3—51no—
207C2×C3×Q8—21no—
208C2×C3×Q8—21no—
209C2×C3×Q8—42no—
210C2×C3×D4—21no—
211C2×C3×D4C22⋊D511yescharacteristic
212C22×C3×C4—21no—
213C22×C3×C4C22×D511yescharacteristic
214C2×#67—101no—
215C2×#67—101no—
216C22×Dic3—51no—
217C22×Dic3—101no—
218C22×Dic3—101no—
219C2×Dic6—51no—
220C3×SD16—42no—
221C2×C3×C8—21no—
222C3×C4⋊C4C22⋊D511yescharacteristic
223C3×C22⋊C4—21no—
224#217—101no—
225#217—101no—
226#216—202no—
227(C2×D3)⋊C4—101no—
228(C2×D3)⋊C4—101no—
229(C2×D3)⋊C4—101no—
230(C2×D3)⋊C4—101no—
231(C2×D3)⋊C4—202no—
232C4⋊Dic3—51no—
233C4⋊Dic3—101no—
234Dic3⋊C4—101no—
235C4×Dic3—101no—
236C2×C3⋊C8—101no—
237C23×C5—21no—
238C23×C5D3×D411yescharacteristic
239C22×D5—61no—
240C22×D5—61no—
241C22×D5—61no—
242C22×D5—121no—
243C22×D5—121no—
244C5×Q8—22no—
245C5×Q8—22no—
246C5×Q8—41no—
247C5×Q8—41no—
248C5×D4—41no—
249C5×D4—41no—
250C5×D4—41no—
251C2×C4×C5—22no—
252C2×C4×C5—21no—
253C2×C4×C5—41no—
254C2×C4×C5—41no—
255C2×C4×C5—41no—
256C2×C4×C5D3×D411yescharacteristic
257C2×C4×C5C2×#6711yescharacteristic
258C22⋊D5—241no—
259C22⋊D5—241no—
260C2×Dic5—61no—
261C2×Dic5—61no—
262C2×Dic5—61no—
263C2×Dic5—121no—
264C2×Dic5—121no—
265C2×Dic5—121no—
266C2×Dic5—121no—
267C2×Dic5—241no—
268Dic10—121no—
269C5×C8—41no—
270#168—121no—
271C22×Q8C2×D1511yescharacteristic
272C2×Q16—301no—
273C2×SD16—21no—
274#126—301no—
275#124—301no—
276#123—301no—
277C22⋊Q8—151no—
278#121—301no—
279#121C2×D1511yescharacteristic
280#120—301no—
281C4×D4—301no—
282C2×C22⋊C4—151no—
283C2×C22⋊C4—301no—
284#103—21no—
285#103—301no—
286C22⋊C8—151no—
287C22⋊C8C2×D1511yescharacteristic
288#95—151no—
289#95—301no—
290C2×C3×C5—21no—
291C2×C3×C5—21no—
292C2×C3×C5—81no—
293C2×C3×C5#45211yescharacteristic
294C2×C3×C5#45511yescharacteristic
295C2×C3×C5B(4,𝔽2)11yescharacteristic
296D15—81no—
297C23×C3—21no—
298C23×C3D4×D511yescharacteristic
299C22×D3—101no—
300C22×D3—101no—
301C22×D3—101no—
302C22×D3—201no—
303C22×D3—201no—
304C3×Q8—22no—
305C3×Q8—22no—
306C3×Q8—41no—
307C3×Q8—41no—
308C3×D4—41no—
309C3×D4—41no—
310C3×D4—41no—
311C2×C3×C4—22no—
312C2×C3×C4—21no—
313C2×C3×C4—41no—
314C2×C3×C4—41no—
315C2×C3×C4—41no—
316C2×C3×C4D4×D511yescharacteristic
317C2×C3×C4C2×C22⋊D511yescharacteristic
318#67—401no—
319#67—401no—
320C2×Dic3—101no—
321C2×Dic3—101no—
322C2×Dic3—101no—
323C2×Dic3—201no—
324C2×Dic3—201no—
325C2×Dic3—201no—
326C2×Dic3—201no—
327C2×Dic3—401no—
328Dic6—201no—
329C3×C8—41no—
330C3⋊C8—201no—
331C22×C5—21no—
332C22×C5—21no—
333C22×C5—41no—
334C22×C5—41no—
335C22×C5—41no—
336C22×C5#91511yescharacteristic
337C22×C5#91611yescharacteristic
338C22×C5#93711yescharacteristic
339C2×D5—122no—
340C2×D5—121no—
341C2×D5—121no—
342C2×D5—121no—
343C2×D5—241no—
344C4×C5—21no—
345C4×C5—21no—
346C4×C5—41no—
347C4×C5—42no—
348Dic5—121no—
349Dic5—121no—
350Dic5—121no—
351Dic5—241no—
352C24—151no—
353C2×Q8—21no—
354C2×Q8—21no—
355C2×Q8—42no—
356C2×Q8—151no—
357C2×D4—21no—
358C2×D4—301no—
359C2×D4—301no—
360C2×D4#122011yescharacteristic
361C22×C4—21no—
362C22×C4—151no—
363C22×C4—301no—
364C22×C4—301no—
365C22×C4C22×D1511yescharacteristic
366Q16—602no—
367SD16—42no—
368C2×C8—21no—
369C2×C8—301no—
370C4⋊C4—151no—
371C4⋊C4—301no—
372C4⋊C4—301no—
373C4⋊C4#122011yescharacteristic
374C22⋊C4—21no—
375C22⋊C4—301no—
376C22⋊C4—301no—
377C22⋊C4—301no—
378C22⋊C4—301no—
379C22⋊C4—301no—
380C22⋊C4—301no—
381C22⋊C4—602no—
382C42—301no—
383C3×C5#160611yescharacteristic, complemented, Hall
384C22×C3—21no—
385C22×C3—21no—
386C22×C3—41no—
387C22×C3—41no—
388C22×C3—41no—
389C22×C3#406111yescharacteristic
390C22×C3#406211yescharacteristic
391C22×C3#408311yescharacteristic
392C2×D3—202no—
393C2×D3—201no—
394C2×D3—201no—
395C2×D3—201no—
396C2×D3—401no—
397C3×C4—21no—
398C3×C4—21no—
399C3×C4—42no—
400C3×C4—41no—
401Dic3—201no—
402Dic3—201no—
403Dic3—201no—
404Dic3—401no—
405C2×C5—21no—
406C2×C5—21no—
407C2×C5—81no—
408C2×C5#503211yescharacteristic
409C2×C5#517311yescharacteristic
410C2×C5#520211yescharacteristic
411D5—241no—
412C23—21no—
413C23—301no—
414C23—301no—
415C23—301no—
416C23—601no—
417C23—601no—
418C23D4×D1511yescharacteristic
419Q8—22no—
420Q8—22no—
421Q8—41no—
422Q8—41no—
423Q8—601no—
424D4—41no—
425D4—41no—
426D4—41no—
427D4—1201no—
428D4—1201no—
429C2×C4—22no—
430C2×C4—21no—
431C2×C4—41no—
432C2×C4—41no—
433C2×C4—41no—
434C2×C4—301no—
435C2×C4—301no—
436C2×C4—301no—
437C2×C4—601no—
438C2×C4—601no—
439C2×C4—601no—
440C2×C4—601no—
441C2×C4—1201no—
442C2×C4D4×D1511yescharacteristic
443C2×C4C2×#122011yescharacteristic
444C8—41no—
445C8—601no—
446C2×C3—21no—
447C2×C3—21no—
448C2×C3—81no—
449C2×C3#6532111yescharacteristic
450C2×C3#6546211yescharacteristic
451C2×C3#6549111yescharacteristic
452D3—401no—
453C5#7097311yescharacteristic, complemented, Sylow
454C22—21no—
455C22—21no—
456C22—41no—
457C22—41no—
458C22—41no—
459C22—602no—
460C22—601no—
461C22—601no—
462C22—601no—
463C22—1201no—
464C22#9180411yescharacteristic
465C22#9180511yescharacteristic
466C22#9182611yescharacteristic
467C4—21no—
468C4—21no—
469C4—41no—
470C4—42no—
471C4—601no—
472C4—601no—
473C4—601no—
474C4—1201no—
475C3#1060176611yescharacteristic, complemented, Sylow
476C2—21no—
477C2—21no—
478C2—81no—
479C2—1201no—
480C2#1175113311yescharacteristic
481C2#1175127411yescharacteristic
482C2#1175130311yescharacteristic
subgroupG/H
centerC22#91826
commutator, cosocleC22×C3×C4×C5C23
FrattiniC22×C4C22×D15
FittingC3×C5×#448C2
socleC22×C3×C5#120
prime radical#11756376C2
hypercenter#448D15
hypocenterC3×C5#1606
LCSG ▷ C22×C3×C4×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ #448

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C3×C5×#448C2semidirect
3. #11751332C2semidirect
4. #11751329C2semidirect
5. #11746358C2semidirect
6. #11746289C2semidirect
7. #11746288C2semidirect
30. C5×#448D3semidirect
68. C3×#448D5semidirect
180. #448D15semidirect
383. C3×C5#1606semidirect
453. C5#70973semidirect
475. C3#10601766semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#117563762
C3×C5×#4482
#117513322
#117513292
#117463582
#117462892
#117462882
#106017663
#709735